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I am considering building complete walls and ceiling out of 3/4" MDF inside this room with 2-3 inches of air space between the MDF and the drywall walls and ceiling. I would build this free standing on the carpet and slab foundation, but not actually attached to the walls or ceiling and seal all the cracks with calk.
A room in a room is the cheapest and actually uses the least amount of space to achieve the type of isolation you seem to require. For a true MSM system, I made an easy to use calculator.
Gregwor & audiomutt’s MSM Transmission Loss Calculator Version 2.03
You can mess with different types of materials at different thicknesses and at different distances from one another to quickly see how much isolation you will achieve (under perfect build conditions of course).
The concern I have with your plan is that you say you don't have room for a room in a room construction but then you say that you do plan to build a room in a room out of MDF. Well, you will still need appropriate framing in order to mount the MDF. At an 11' span, I'm guessing that you're going to need to use at least 2x8 joists. So that lowers your ceiling 7 1/4" plus 3/4" for your MDF plus the gap between your existing ceiling and your new joists (let's just say 2" for fun). So, now you are 10" lower.
This isn't the worst. I assume you have some sheathing on your existing ceiling. What you should do is remove that sheathing exposing your joists and subfloor above. This will give you a bigger gap between your outer leaf and your new ceiling. If you then build your new ceiling using John Sayer's inside out method, you will only lose ~2 3/4" of height! Not bad right!?? Now, this is the acoustic height of your room. Visually, you will still be 10" lower. But, are you concerned about how it looks or how it sounds? Clearly, how it sounds is more important. To put your concerns at ease, check out my buddies little drum practice room. He faced the exact same issues as you and with the black fabric on the ceiling, it feels way taller in there than it actually is. And it sounds killer too:
http://www.johnlsayers.com/phpBB2/viewt ... =1&t=21704
My theory is that the MDF would stop more of the low frequency trying to get in. The air space would help and the fact that it is not attached to the existing structure would prevent the sound waves from resonating between the 2 structures.
There is actual theory on how to achieve isolation. I encourage you to dig through this literature before you tackle any major construction as having some knowledge about the topic will save you a lot of money and get you the results that you're after!
http://www.roletech.net/books/HandbookAcoustics.pdf
Also, if you have any links 2 sites that would give me some low cost D.I. Y. acoustic design idea, I would greatly appreciate it.
By acoustic design do you mean isolation or treatment? It sounds like you have an isolation problem so everything I wrote above should get you started.
Greg